Nowadays, optical methods are widely used for measuring or determining characteristics of objects, and in particular for measuring the three-dimensional contours of objects. One preferred optical method is a so-called optical triangulation method wherein the object to be measured is moved in relation to a measuring system which includes a light source and a sensor. Optionally, the object is stationary and the measuring system instead moves in relation to the object. Furthermore, optics are generally located between the sensor and the object for focusing light reflected from the object onto the sensor. The light source, the object and the sensor are located at a distance from one another such that they each form a corner of an imaginary triangle, hence the name optical triangulation. During each time instant in a set of at least two subsequent time instants, the sensor generates an image of the object based on light emanated from the light source and reflected from the object, thus generating a set of images. Each image is generally constituted by a set of pixels arranged in a matrix having rows and columns wherein each column generally corresponds to a direction perpendicular to a direction in which the object is moved in relation to the measuring system. A three-dimensional image of the object is then created by analyzing the light intensities in the set of images.
Originally, the aforesaid analysis was limited to scanning each one of the generated images for peaks in the light intensities and generating a three-dimensional image of the object based on the positions of the intensity peaks, i.e. in which image as well as in which part of the image each peak occurs. However, it can be shown that the aforesaid analysis gives a correct three-dimensional image of the object only when the object is perfectly planar and has a uniform reflectivity.
Since a method of creating a three-dimensional image of an object which uses the assumption that the object is perfectly planar seems rather contradictory, improvements of the original optical triangulation method have been proposed.
One improved method of interest for the present invention is disclosed in a paper by B. Curless and M. Levoy, namely “Better Optical Triangulation through Spacetime Analysis” in IEEE International Conference on Computer Vision, pages 987-994, Stanford University, June, 1995. The aforesaid paper discloses an optical triangulation method wherein space-time images are generated for each column of a set of images. As previously indicated, each image has a row dimension and a column dimension; hence each column space-time image has a row dimension and a time dimension. It should be noted that if the space-time images for all of the columns were to be assembled, a space-time volume would be obtained having a column dimension, a row dimension and a time dimension.
B. Curless et. al. further teaches that an enhanced three-dimensional image may be obtained by a scanning procedure comprising the steps of rotating each space-time image by a predetermined angle, which angle is generally denoted the space-time angle, before scanning each row in the rotated space-time image for light intensity peaks. The position of the peaks, in both the row and time dimension, is then rotated back to the original coordinates. Optionally, the scanning procedure above may be described as analyzing the light intensity along trajectories in each space-time image, which trajectories typically are assumed to be straight lines inclined by the space-time angle.
According to B. Curless et. al., the scanning procedure disclosed hereinabove provides for a three-dimensional image generating method which is more robust than the original method. For instance, the scanning procedure is less sensitive to variations in reflection properties of the object. Furthermore, sharp corners and/or end points of an object may be more correctly imaged when using an optical triangulation method including the aforementioned scanning procedure than when using the original method.
B. Curless et. al. further teaches that the predetermined angle by which the space-time image should be rotated can be calculated analytically based on a formula having inter alia the geometrical and optical relation between the sensor and the object as well as the motion of the object as input.
However, when deriving the aforementioned formula for the space-time angle, some assumptions are required e.g. that the sensor is orthographic and that the object moves with a constant velocity in relation to the measuring system during the execution of the optical triangulation method.
Furthermore, the analytically derived space-time angle does not account for secondary effects, such as secondary reflections and/or imperfections of the optics generally connected to the sensor.
As may be realized from the above, there is a need for improving the method of obtaining light intensity trajectories in a space-time image or, more generally, in a space-time volume, which method is not based on the limiting assumptions in B. Curless et. al. and/or which method is adapted to account for secondary effects and/or which method enables that an optical triangulation method, utilizing the obtained trajectories, may use a varying, i.e. not constant, velocity of the object in relation to the measuring system.